RECENT MÖSSBAUER EFFECT STUDIES IN
INTERMETALLIC AND RARE-EARTH
COMPOUNDS
W. Zinn
To cite this version:
W. Zinn. RECENT MÖSSBAUER EFFECT STUDIES IN INTERMETALLIC AND RAREEARTH COMPOUNDS. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-724-C1-730.
<10.1051/jphyscol:19711251>. <jpa-00214081>
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JOURNAL DE PHYSIQUE
Colloque C I, supplkment au no 2-3, Tome 32, Fkvrier-Mars 1971, page C 1 - 724
RECENT MO SSBAUER EFFECT STUDIES
IN INTERMETALLIC AND RARE-EARTH COMPOUND S
W. ZINN
Siemens AG, Research Laboratories, Munich, B. R. D.
Rksumk. - De rkcentes ktudes par Effet Mossbauer (E. M.) et par R. M. N. d'interactions hyperfines (h. f.) entre
151(153)Eu et Eu2+ dans des composks EuX (X : 0,S, Se, Te) et d'ktudes d'E. M. d'interactions h. f. entre 166Er et Er3f
dans des composks (Erl-xXx)Alzet ErNiz-zCox a structure de Laves (X : Y, Gd) rkvklent dans les deuxcas deremarquables transferts d'interactions h. f. Des champs h. f. intrinskques et transfkrks ont 6th mis en evidence et quelques corrklations et dkpendances entre les grandeurs magnktiques, hyperfines et la nature des liaisons ont kt6 reconsidkrkeset complktkes.
Abstract. - Recent Mossbauer effect (M. E.) and NMR studies of 151(153)Eu/Eu2+hyperfine (h. f.) interactions
with EuX-compounds (X : 0,S, Se, Te) and M. E. studies of 166Er/Er3+h. f. interactions with (Erl-xXx)Alzand ErNiz+
Cox Laves-structures (X : Y, Gd) revealed significant transferred h. f. interactions in both cases. Intrinsic and transferred
h. f. fields have been seperated and certain systematics and correlations between magnetic, bonding, and h. f. data reconsidered and completed.
Introduction. - Among arich variety of interesting
and fundamental magnetic properties displayed by
rare-earths and their compounds [I] especially two
characteristic features necessitate zero applied field
studies by means of microscopic tools suchas nuclear
resonance and neutron diffraction techniques :
1) Unusual large anisotropy energies due to large
unquenched orbital moments,
2) Rather complicated spin-structures and the
appearance of different ordered magnetic phases due
to a competition between different indirect 4f-4fexchange interactions.
The basic problem with nuclear resonance techniques
still is to establish unambiguous relations, which can
be used to deduce the effective magnetic moments of
distinct atoms with zero applied field and unaffected
by anisotropy and spin-structure from the measured
hyperfine interaction energies.
This paper is partly a report on some recent results
obtained with Eu2+ ions in Europium-chalcogenides
using l5'Eu and ls3Eu nuclei and with intermetallic
Erbium-compounds using 166Er-nuclei. It is also
partly a review of Mossbauer effect and n. m. r. work
on these compounds.
With these examples a large body of magnetic,
optical and hyperfine (h. f.) data has been accumulated
in recent years. This will enable us to establish and
complete certain systematics, which lead to an improved
understanding of the relations used in Mossbauer
effect (M. E.) studies of rare earths so far and already
reviewed by Ofer [2], and Wickman [3].
I. 151(153)E~/E~2f
hyperhe interactions in EuroON MAGNETIC AND
pium-chalcogenides. - 1.1 SURVEY
HYPERFINE INTERACTIONS IN EuX COMPOUNDS. - First
we remind of some significant relations. With S-state
ions such as Eu2+ the h. f. field at a lattice site i is
given by (I)
(1) Hyperfine fields here are given in the internationally
recommened B-units cr Tesla >> (IT = lO4G = 1 Vsm-z), which
fortunately differ by only a factor of 10 from the so far utilized
H-units kOe.
B ,=
~ (A:,,,
< S, >, +
+ A;),
+
z (A%,
$-
j+i
AvaJj
< S, >
(1)
j
B, is mainly due to the core- and, conduction-s-electron
polarization by the atom's own spin Si [4], but with
concentrated magnetic sublattices as a rule is contributed significantly by transferred h. f. fields due to
conduction and valence electron polarization by the
neighbouring spins S j . The magnitudes of the involved
h. f. coupling constants are about A$,,, z 10 T,
A", and A,,, FZ _+ 1 T. At finite temperatures the average
value < S, > of the atomic spin component along the
local magnetization direction z and related to the
effective magnetic moment < p > = g, p < S, >
rather than S appears, because the spin correlation
time zs (due to rapid thermal fluctuations of S between
its eigenstates S, ranging from - S to -t S) usually is
by orders of magnitude smaller than the nuclear
Larmor period z, = h/AS 131. While AScannot be calculated for magnetic solids, precise zero field measurements of sublattice magnetizations m(T) = M(O/M(O)
nevertheless are possible, if A"(T)/A"O) z 1 holds or
has been measured. As discussed previously [5] this
proves true with EuX-compounds and enables one to
deduce the data plotted in figure l b for J,, J2, and
Tc from the appropriate theoretical relations (such as
B,(x), (1 - aT3I2), or ((1 i. e. the molecular
field and low temperature spin-wave approximations,
or the scaling law (at T T,), respectively). Recent
detailed M. E. studies of the nature of phase transitions
in EuO by Groll [6] and with EuSe by Petrich [7]
should be mentioned. In particular, P = 0.34 0.02
and Tc = (69.19
0.02) K has been found with EuO,
while with EuSe [7] the first order phase transition
suggested by Kuznia [8, 51 from a combined magnetic
and n. m. r. study has been confirmed. In the following
discussion only zero-temperature values of B,(O) being
related to S are used.
u
in two Eu2+-compounds of
Between 1 5 1 ~ nuclei
s-electron densities L,(O) and L2(0) the isomer shift
5
+
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711251
+
with respect to a certain gamma ray source (e. g.
lS1Sm in Sm203) is given by [9]
(Ze nuclear charge, 6 < r2 > difference of charge radii
between the nuclear ground and excited state involved
in the Mossbauer transition.) Table 1 summarizes all
nuclear data useful in this discussion.
Nuclear Data (") of the Isotopes 1 5 1 ~ u ,1
and 166Er
Natural Isotope
Abundance : ( %)
Spins I, : (fi)
re : (fi)
Magn. Moments
pg : (n. in.)
, ~ e: (n. m.)
Quadrupole Moments
Q, : (b)
(1 -RQ)Qe : (b)
47.77
512
712
5 3 ~ ~ ,
-
-
52.23
512
712
32.9
0
2
3.439 1
2.57
1.518 6
3.21
1.18(2)
1.5
2.95(2)
-
0
0.63
0
- 1.6
(fi = 1.054 5 x 10-34 VAs2, l(n. m.) = 5.050 5 x 10-27VAsT-1
l(b) = 10-24 cm2, l(fm)2 = (10-13 cm)2
(a)
E. g. see OFER [2].
The magnetic, electric, and optical properties of the
EuX magnetic semiconductors (X : 0, S, Se, Te)
discovered with EuO in 1961 have been extensively
reviewed recently [lo, 111. Figure 1 summarizes certain
optical and magnetic data also discussed previously [5],
but significant for the intended discussion of
correlations between the magnetic interactions J1and
J2(Fig. lb), the bonding character (ionicity j,,'), and
the h. f. interactions (i. e. isomer shift 6,, and h. f.
field B,(O)) (Fig. lc).
In EuX, the magnetic E u + + ions occupy either of
two f. c. c. sublattices of a cubic rocksalt structure
(space group Fm 3 m - 02) and exhibit a spin-only
moment of nearly 7 ,uB well-localized on the 4f-shell
and having the groundstate 4f7-as7,?.The exchange
interaction- J, is-due to the coupling of a ELI++ ion
to its twelve next Eu-neighbours via an overlap of the
Eu+'-5d-t2,-orbitals, while J2 is due to a superexchange to the six next nearest neighbours via the
overlap of Euf +5d-eg-orbitals with p-orbitals of the
intermediate anion. J, is positive and tends to align
the Eu' +-spins parallel, whereas J2is negative favouring an antiparallel alignment of spins in adjacent
(1 11)-planes. The exchange interactions are related to
the intra-atomic exchange A,, between the 4f- and
5d-electrons and to the attributed electron transfer
and interband energies bi and Ui by relations of the
form Ji = A,, ~;/S,,/U~~.These have been discussed
in more detail by Goodenough [12] and with emphasis
placed on the EuX-compounds by Kasuya 1131recently.
Generally (bi/Ui)' will decrease with increasing Ui
FIG. 1. - Summary of the optical results on band structure
and transition energies of EuX compounds (a), the related
magnetic exchange data (b), and the hyperfine interaction data
(c) as obtained from n. m. r. (e) and M. E. studies (A h. f.
fields,
isomer shifts ; ( 0 ) calculated from EuSe n. m. r. data).
and decreasing overlap integrals (included in b,). The
energies U,(f, d,) and U2(p, d,) necessary to transfer
electrons from either 4f7-levels to 5d-t2g-levels or
from p-levels at top of the valence band into 5d-eglevels, respectively, have been deduced from optical
absorption spectra as reviewed recently by Dimmock
[14]. The dependence of Ui of the lattice constant
(Fig. la) corresponds to that observed with Jl and
J2.The optical gap energy EG, the crystal field splitting
10 Dq between the 5d-t2,-triplet and the 5d-e,-doublet
may give a feeling of the EuX-band structure. With
this background on band and magnetic properties let
us look for correlations with the hyperfine interactions
plotted in figure lc.
1 .2
SYSTEMATICS
OF
s 1 , 1 5 3 E ~ / ~ ~ 2 + - ~ ~
-Several attempts have been made previously to establish correlations between 4,and B,
with EU+"-compounds [15, 161. Due to the omitted
separation between intrinsic and transferred B,-contributions (eq. (1)) they have been partially successful only.
With Europium metal the significance and possibility
of this separation have been clearly demonstrated by
the recent M. E. work of Hiifner and co-workers
[17, 181.
With the EuX-family the recent n. m. r. study of
metamagnetic EuSe by Kuznia [8] revealed the existence and magnitude of transferred hyperfine fields.
As discussed in detail in a previous paper [5], from
these n. m. r. data obtained with EuSe in the ferrimagnetic phase two distinct h. f. fields
INTERACTIONS.
C I - 726
W. ZINN
and
BYO) = -(26.2
+ 0.25) T
attributed to the sublattices N and S have been
deduced. The neutron diffraction results by Fischer
[19] revealed three spin structures in EuSe consisting
of ferromagnetic (I 11)-planes with their magnetization
pointing either north (N) or south (S). Following the
[I 111-axis one observes a NNSS-period with the antiferromagnetic phase, and a NNS-period with the
ferrimagnetic phase in accordance with the magnetic
and n. m. r. results [5, 81. EuTe displays the MnO-spin
structure NSNS [20], while for the ferromagnetic
phase N is assumed. Hence, considering a central
%spin three cases have to be distinguished with respect
to the two adjacent (111)-planes, i. e. NNN, NRS,
S ~ (see
S arrows in Fig. lc and 2). Taking into account
further that 6 n.n. are present in the central KT-plane,
added by 3 n.n. and 3 n.n.n. of each adjacent
(11 1)-plane we arrive at the result, that each configuration differs by 6 n.n. and 6 n.n.n. contributions, i. e.
participation of Sp-electrons to the bond causing a
decrease of screening with the Eu outer s-shells,
However, from band structure and the B,-systematics
to be discussed now, the Eu-5d-electrons should be
related to this effect rather than the 5p-electrons.
In figure 2 the B,-data of M. E. and N. M. R. studies
-
-15
-14
I YsIO)I~INCREASING
ISOMER SHIFT
-12
-11
-10
-13
mmh
-8
-7
-6
FIG. 2. - Summary of intrinsic (B1,i(4f76 so) + 0 )and trans-
From this result and the attributed relations and data
of the observed fields (i. e.
and 32.7 T [5] with EuO and EuS, respectively,
B,(N%s) = BY,,
6 B, = BN(0)and
+
-
with EuSe, and B,(s%s) = B;,~ - 6 AB, = 25.5 T
[21] with EuTe) one obtains an estimate of the transferred fields, and of the intrinsic contributions, i. e.
B:,~ = (AS,,,, AS,,), < Si > E B,(sNs). With these
separated Brcontributions the B, vs a,-plot in figure l c
looks much more systematic than that revealed by the
measured B,-data (full dots in Fig. lc). In figure lc
also &,-data taken from an 15'Eu M. E. study of
Eu2+- and Eu3+-compounds by Gerth 1221 and
B,-data (2) from recent M. E. studies are shown.
From a synopsis of figures la, b, and c the mutual
correlations between isomer shifts, optical, and
magnetic data and also those with the lattice constants
are obvious. In particular, the simultaneous decrease
of EG710 Dq, U,, and jpaccompanied by an increase
of J2 and decrease of J, is mutually consistent and
reasonable. In addition a linear relation between
a,, and the Pauling ionicity [24] exists as pointed
out already in [22].
However, B,,,(a,), i. e. the spin density at the Eunucleus does not seem to fit in these systematics. It is also
not obvious, why the s-electron density L,(O) increases
(i. e. leads to more positive 43 with j, while the
EuX-bonding electrons become increasingly removed
from Eu and concentrated on X. Kienle and coworkers [22] suggested this to be due to an increasing
+
(2) Note that in EuSe the M. E. studies resolve only one
h. f..field, which, however, is found either near BS(-26.8 T 1231)
or near B"(-28.7 T) 171).
ferred(@)h. f. fields from 15l(ls3)Eu/Eu2+-M. E. (A) and
n. m. r. (e) studies of EuX compounds, compared to results
on E u o - and EuX2-metals, and related to isomer shifts 61,
(i. e. s-electron densities at the Eu nuclei), nature of bonding
(ionicity j,), BI-values of atomic spectroscopy obtained with
4f7 6 s 6 p-and 4 f7 6 s2-Eu-configurations, and the ENDOR
result with Eu2+(4f7 6 so) in CaF2.
Erratum : In the figure S and B are like in the text but
without the circle.
are plotted against the attributed isomer shifts. Included
are B,-data deduced by means of atomic spectroscopy [25] and Endor-techniques [26] for the Euconfigurations (4f7 5s' 5p6)-6s2,-6s6 p, -6s0, In addition Wickman's results on EuX,-Laves structures
[16] and Hiifner's results [17, 181 on Eu-metal diluted
with Ca, Sr, Ba, and Yb are plotted. Finally the
complete Pauling ionicity scale as related to Gi,(EuX)
is shown. If one extrapolates the two branches revealed
by the intrinsic fields B:,~(Eux) either between EuS
and EuO or between EuSe and EuTe one obtains
two base lines having a rather suggestive character
with respect to B,-4, and B,-j-correlations. The one
branch is labelled (( S D, since it is closely related t o
s-electron densities and isomer shifts. The second
branch is labelled (( B )), since it is related to the
bonding character and to the h. f. fields B, rather than
to a,,. (( S n intersects with
at
4, = - 14.7 mm/s, passes Hiifner's intrinsic fields
+
Si obtained with Eu in Sr, and Ba and
intersects with B,(4f7 6s2) of the free atom at
4, = - 6.3 mm/s. The base line suggested from the
bonding branch (( B )) intersects with B,(4f7 6s 6p) near
jp = 0 and with B,(4f7) at about j, = 100 %. Hence,
both branches display some reasonable features.
Branch ct S )) related to a,, which in fact is a charge
density scale, suggests (AS,, S)i of eq. (I), i. e. the selectron polarization by the atom's own 4f-shell and
-
RECENT M~SSBAUEREFFECT STUDIES IN INTERMETALLIC AND RARE-EARTH COMPOUNDS C 1 727
labelled
in figure 2, to be correlated linearly with
4,. In particular, the increase of this term from 0
(at 4, = - 14.7 mmls) to 27.2 T (at 4, = - 6.3 mmls)
and the corresponding decrease of B,,i from - 34.2 T
to - 7 T, is seen to be correlated with an increase of
4,. The isomer shift between the 4f7 6s2- and
4f7 6s0-configurationsdeduced from the B,-&,-line cc S )>
is about 8 mm/s and thus differs by a factor 2 from
the value 17.6 mm/s deduced from isotope shifts by
Brix [9]. However, it is in fair agreement with
Aai,(4f7 6s' - 4f7 6s') w 10 mmls obtained from a
recent Hartree-Fock (HFS) calculation [27]. Hence, we
hope that the base line (( S )) will prove to be unique (3).
Since it predicts an estimate of the transferred h. f.
fields (labelled @ in Fig. 2) in EuX,, dilution of Eu
with Yb or Sr e. g. in EuA1, would provide an experimental check of the proposed base line (( S )).
Let us next discuss the probable reasons for the
change from branch (( S 1) to branch ct B )) displayed with
EuX compounds at EuS, but in a similar way also
in Hiifner's results between Eu-Ba(Sr) and Eu-Ca (see
Fig. 2 and [18]). The B,,i-term (A:, S)i of eq. (1) is
found to increase again, while 4, and L, are further
decreasing. Hence, there must be an additional contribution to @ not related to the s-electron density.
The apparent correlation of this branch with j, and
the fact that with a pure covalent EuX-bond (j,, = 0)
the attributed (extrapolated) h. f. field corresponds to
that of the 4f7 6s 6p configuration suggests bonding
p- and s-electrons being shared nearly equally between
Eu and X. However, comparing the branches (( S )> and
B )) with J, and J2in figure Ib, a correlation of J,
with (( S )) and of J2with (( B )) is cogent. This suggests
the increase of term (A:, S)i on branch B to be related
to increasing overlap and transfer between anion p- and
cation 5d-e,-orbitals causing both the bonding an the
superexchange J2.The increasing s-electron density at
equivalentlywould be relathe Eu nucleus on branch ctS~
ted to the increasing overlap of 5d-t,, orbitals between
neighbouring Eu atoms thus causing additional bonds
together with the exchange interaction J,. The participation of 5d-tg2orbitals in bond and exchange would
decrease the shielding of the outer Eu-s-electrons and
hence cause the observed increase of L,(O).
To summarize : Strong correlations between the h. f.
interactions, electron densities and nature of bonds,
band structures, and exchange interactions have been
detected by the systematics proposed and discussed
here and are waiting for further experimental checking
and an improved theoretical understanding now.
h. f. interactions in Er-A1 intermetallic
2. 166Er/~r3+
compounds. - 2.1 SIGNIFICANTRELATIONS FOR
1 6 6 E r / ~ r 3H.
+ F. INTERACTIONS. - In this section
we will discuss recent M. E. sttudies with a typical
non S-state rare-earth ion, Er3+,which demonstrate
that the usual neglection of transferred h. f. fields is not
justified in intermetallic compounds of heavy rareearths such as Er.
(3) Note, that by relying on cr S >> and deducing 6is from the
magnetic h. f. splittings the experimental error of 6is would
be due to ABzr instead of 2 rex
(shown in fig. 2) and thus
could be reduced.
J = L + S now is expected to be a good quantum
number. The Er3' groundstate is
4f1' - 4115,2
(L = 6, S = 312, J = 1512) and corresponds to a magnetic moment < p > = gJ pB < JJ,>,
where g, is the Lande factor (gJ = 615 with Er3+).
< J, > again is the thermal average over the 2 J + 1
eigenstates of J, responsible for the temperature
dependence of the magnetization as given by
m ( 0 = < J, >lJ = Tr(J, p)lJITr p,
where
p = exp(- Jzg, p, H,,,(T)/kT) is the density matrix
for the molecular field (Heff(T))approximation.
The h. f. field given by eq. (1) is to supplement now
by another contribution
resulting in a total field of
Since A,, w 100 T, B4, is the dominating contribution
here, whereas the A: give rise to only a correction of a
few percent and Aj so far has been assumed negligible.
We will see, however, that this is not admissible
generally, since in certain cases Aj/A4, -- 0.05 may be
obtained. For the temperature dependence (under the
presumptions made already with S-states) again
BI,~(T)IBI,
i(O) = Heff(QIHeff(0) =
= Mi(T)/Mi(0) = Tr(J, p)/JTrp
is expected to hold. In addition to the case of S-states
the term B,, is always accompanied by an temperature
dependent electric field gradient (e. f. g.) at the r. e.nucleus. It is given by
and exists also with cubic lattice symmetry, where the
lattice term q,,,,(l - y,) of the total e. f. g.,
vanishes (RQ and y, are Sternheimer's shielding and
antishielding factors [2]). Using an operator equivalent
method B,, and q,, have been calculated by Elliot and
Stevens [2, 281 to
The matrix elements of r-3, N, and a are tabulated [2, 281 and yield 10.60 x a t 3 , 0.78, and 11400,
respectively, for Er3+.
For the 80.6 keV (2'- 0) transition used in 166Er
M. E. experiments (see Table 1) the energy of the five
transitions (mI = - 2, - 1, ..., + 2) are given by
AE(m,) = E(m,) - E, = Am,
+ 3 ~ ( m ;- 2)
(5)
where from eq. (3), (4), and table 1 the relations
between the magnetic and quadrupole coupling
Hamiltonian (Ed. For the other limit, X, 9 X,,,
the usual, equally spaced (2 J 1)-multipletis expected
with < J, >, = - J = - 1512 lying lowest and
A4,(0)/(cm/s) = 3.646 5 x 10- B4f(0)/(T)
yielding < p >, = 9 ,L+,. This groundlevel is also
= 0.374 < J, >, = 0.312 < p, >o/@B)
expected with a splitting into eight Kramers doublets
and
1512 > is lowest in
in a non-cubic c. f. where I
energy.
r E. spectra for pure and
In figure 3 the 1 6 6 ~M.
Y-substituted Er-Al-compounds are shown [30, 311 for
We are interested in < J, >, for Er3+ at a given lattice the lowest temperatures used. Between ErAI, and
site with cubic symmetry here, i. e. in cubic Laves- ErAI, apparently the h. f. splittings differ by nearly a
structures RX, (space group Fd 3 m-o:,
MgCu2- factor 2 and so do the T,-values and the < p >-data
C 15-type) and in cubic RX,-structures (space group deduced from the M. E. spectra by means of eq. (3)
to (5). Substitution of Er by Y causes a pronounced
Pm 3 m-o;, Cu,Au-L1,-type).
decrease of T, and B,,i (i. e. < p >i)as can be seen
In RX, each R is surrounded tetrahedrally by four from figures 3 and 4. In addition, significant line
R-n. n. being e. g. in ErAI, 0.337 nm apart. In RX,
each R is surrounded by twelve X-n. n. being (with
ErA1,) 0.298 nm apart from R while the six R-n. n. n.
form an octahedron and are 0.421 nm apart. Hence, the
transferred h. f. fields, if any, in RX, would beexpected
to be smaller than in RX,. In both cases we have R,+
in cubic symmetry. Thus, due to LEA [29] after splitting of the Er3+ groundstate J-manifold by the crystal
field (c. f.) a T,-quartet or a r,-doublet is expected to
lie lowest with ErAl, and ErAl,, respectively. The
lower limit of < J, >, and < p >, then are the rsvalues, i. e. < J, >, = 4.6 and < p >, = 5.5 &p,.
This presumes the c, f. splitting Hamiltonian (X,,) to
be large with respect to the magnetic exchange splitting
constants (A and P, respectively) and BlPi(O) or
< J, >, can be calculated to
+
+
FIG.4. - Summary of Er3+-magnetic moments obtained from
neutron diffraction (+), bulk magnetization measurements (w),
and comparison with 166Er h. f. data (A). Proposed corrections for Er-Er and Er-X (X : Co, Fe) transferred h. f. fields
are labelled (@ Q) and (@), respectively. Abscissa is the substitution x in (Erl-zXz)A12 (X : Y , Gd). The systematics of h. f.
data revealed by these two series of Laves-structures by the
drawn lines have been used to locate abscissa for the other
examples with respect to their splitting data.
I
-6
I
-4
I
-2
I
0
VELOCITY V
1
2
I
4 cmh
8
FIG. 3. - 166Er M. E. spectra of different Erbium-Aluminium
intermetallic compounds. (With Erl-,Y2AI2 spectra for
nl = 0,1,.., 4 Y-n. n., and with ir-ErAls with two sublattices are
drawn. Typical Er3+ spin relaxation effects have been observed at
highertemperatures only as analyzed in [30,31Jand can be ruled
out for the low temperature spectra shown here.)
broadenings and structures are revealed. They are due
either to changes of the intrinsic B,-term because of
different moments < p > ior to changes of the sumterm of the transferred h. f. fields, both caused by the
now given distribution of different local Er-Y-environments. The same question arises with the two inequivalent sublattices displayed by a-ErAl, [32, 331.
Neutron diffraction data on < p >, are required to
distinguish between the two possibilities and are under
way. The so far available results are plotted in figure 4
[34, 351. In a- and P-ErA1, and in Er, -,Y,Al2 the
B,(n,) and q:F(n,) data attributed to n, = 0, 1,2, 3,
and 4 Er-n. n. substituted by Y have been deduced
from these M. E. spectra by means of a computer
fit [30, 311. The results are plotted in figure 4 against
the Er-substitution x. In order to reveal possible systematics of the h. f. data, in figure 4 related andsignificant ' 6 6 ~ r / E r 3 +h. f. data have been compiled, e. g.
the data obtained by Purwins [36] on the Er, ,GdXAl2
series and by Petrich [37] on ErNi, ,Cox compounds.
The distinct ErX2-families have been located on the
abscissa in such a way that B,, P, < ,u > and Tc(N)
increase monotonously from the left to the right. In
addition the results by Hiifner [38] on Er-metal, by
Cohen [39] on ErFe,, and by Weber [40] on 1.5 % Er
diluted in b. c. c. iron are included. The < p >,-data
deduced from the M. E.-data are to be compared with
recent results of bulk magnetization measurements
available with ErAI, 136, 41, 421, ErAI, [43],
ErNi,,Co,
[37, 441, ErFe, [45], partially reviewed
already by Bozorth [46]. In compounds displaying a
ferrimagnetic or still more complicated spin structures
it is meaningful to compare the M. E. results with
< p(Er) > deduced from neutron diffraction (N. D.)
studies rather than with bulk magnetization. Recent
[35],
N. D. data available for P-ErAI,, Er,,,Y,.,AI,
ErAl, [34], ErCo, [47], and Er [48] are plotted in
figure 4. As a rule, the microscopic methods so far
yielded much higher < p >,-values than bulk magnetization measurements.
In fact, as in the case of Eu-compounds, the compilation of magnetic and h. f, data in figure 4 again
reveals certain systematics and correlations, which
lead us to some significant conclusions on intrinsic and
transferred h. f. interations :a) As expected, it becomes
obvious from figure 4 that the influence of the c. f. and
attributed quenching of < p(Er) > increase from the
right to the left side with decreasing T,(,) and hence
decreasing magnetic exchange splitting of the Jmanifold. b) The slope of < p >, against substitution x revealed by the N. D. data is much smaller than
that observed with the h. f. fields and attributed
< p >,-values. Hence, the variations of < p >,
revealed by N. D. data can only partially account for
either the observed decrease of B, with magnetic
dilution of the Er-sublattice by Y or for the enhanced
increase of BI with substitution of the non-magnetic X
atoms (e. g. Al) by transition elements (e. g. Fe, Co).
Thereby, the remaining AB, have to be attributed to
transferred h. f. fields. In Er, ,YXAl2 these transferred
h. f. fields at an central Er-atom with all four Er-n. n.
substituted by Y (labelled in Fig. 4) are found to be
about 120 T, i. e. AB, = 30 T/(Er n. n., 0.337 nm
apart). Hence, if one attributes this reduced B,-value
(770 - 120 = 550 T) to the intrinsic term ( c i >i) in
eq. (3) (i. e. to the contribution which in fact is related
to < p >, by the eq. (3) to (5)) then one can again
draw a base-line for this term, which runs parallel to
that obtained for the N. D. data. The M. E. data for
< ,u >, deduced from these separated intrinsic fields
B,,i % B4,,i then are seen to be much smaller than
those deduced so far from B, instead B,,i. The < p
now are closer to the bulk magnetization values than
to the N. D.-data. They further reveal considerable c. f.
quenching of < ,u >, for all examples and show that
with P-ErAI, the r8-c. f. value for < ,u >, is nearly
obtained. Note that with this example the transferred
h. f.-field of - 80 T (labelled 0)has changed sign and
yields AB, x - 13 T/(Er n. n. n., 0.421 nm apart).
The transferred h. f. fields due to the substitution of Al
by Co or Fe (labelled O ) reach about
64 T for Er
in b. c. c. Fe, i. e. AB,(Fe) z 8 T/(Fe-n. n.).
The mechanism responsible for such large ABj is
still unknown. However, since the quadrupole splittings
P shown in figure 4 reveal the same behaviour as BI
just discussed, and, in particular, since also transferred
e. f. gs.
q;" are indicated, at least with the Er-substitutions
s-electron spin-polarization seems to be ruled out.
On the other hand, spin-orbit-couplings between
conduction electrons and the rare-earth cations have
been shown by Levy [49] to be significant and necessary
for the understanding of the T,-systematics of the RX2series of compounds. In fact, this mechanism could
account also for AB, and AB,. The contributions ABg
have been observed previously between GdA1, and
GdFe, by Gegenwarth [50] and related to valence
electron polarization. In any case, the ABj are again
found to be significant and closely related to bonding
and exchange contributions by electrons, which
display either p- or d-character.
+
Conclusion. - For two typical cases, i. e. 151(153)E~/
Eu2+ (S-state) in EuX and 166Er/Er3+(J-groundstate)
in Er-intermetallic compounds, it has been shown that
significant transferred h. f. interactions exist. They
necessitate a reanalysis of the conclusions made so far
on Er3+ ionic magnetic moments and enable one to
separate between intrinsic and transferred h. f. interactions. Taking this into account systematics for both
contributions can be established. The intrinsic part
is shown to be related to the ionic moments while the
transferred contributions and isomer shifts are shown
to be closely correlated mutually and with the nature
and strength of bonds and exchange interactions. This
opens new possibilities for using the M. E. as a microscopic tool for the study of bonds and interactions in
magnetically concentrated and ordered solids.
Acknowledgement. - I would like to thank G.
Will, H. J. Jackel, and K. Weber for providing me with
unpublished neutron diffraction and M. E. data.
Further I gratefully acknowledge an illuminating
discussion with G. M. Kalvius on recent M. E. work
and related HFS-calculations concerning the
15'Eu/Eu2+ h. f. interactions.
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